Download IO Class note 10：Dynamic Games and First and Second Movers

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IO Class note 10：Dynamic Games and First and Second Movers
Introduction
• In a wide variety of markets firms compete sequentially
one firm makes a move: new product/advertising
second firms sees this move and responds
• These are dynamic games
may create a first-mover advantage or may give a second-mover advantage
may also allow early mover to preempt the market
Can generate very different equilibria from simultaneous move games
Stackelberg
• Interpret first in terms of Cournot
• Firms choose outputs sequentially
leader sets output first, and visibly
follower then sets output
• The firm moving first has a leadership advantage
can anticipate the follower’s actions
can therefore manipulate the follower
• For this to work the leader must be able to commit to its choice of output
Stackelberg equilibrium
• Assume that there are two firms with identical products
• As in our earlier Cournot example, let demand be:
P = A – B.Q = A – B(q1 + q2)
Marginal cost for for each firm is c
Firm 1 is the market leader and chooses q1
In doing so it can anticipate firm 2’s actions
So consider firm 2. Residual demand for firm 2 is: P = (A – Bq1) – Bq2
Marginal revenue therefore is: MR2 = (A - Bq1) – 2Bq2
Work on yourself….
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Stackelberg and commitment
• It is crucial that the leader can commit to its output choice
without such commitment firm 2 should ignore any stated intent by firm 1 to produce (A – c)/2B units
the only equilibrium would be the Cournot equilibrium
• So how to commit?
prior reputation
investment in additional capacity
place the stated output on the market
• Given such a commitment, the timing of decisions matters
• But is moving first always better than following?
• Consider price competition
Stackelberg and price competition
• With price competition matters are different
first-mover does not have an advantage
suppose products are identical
suppose first-mover commits to a price greater than marginal cost
the second-mover will undercut this price and take the market
so the only equilibrium is P = MC
identical to simultaneous game
now suppose that products are differentiated
perhaps as in the spatial model
suppose that there are two firms but now firm 1 can set and commit to its price first
we know the demands to the two firms and we know the best response function of firm 2
The Example
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Dynamic games and credibility
• The dynamic games above require that firms move in sequence
and that they can commit to the moves
reasonable with quantity
less obvious with prices
with no credible commitment solution of a dynamic game becomes very different
Cournot first-mover cannot maintain output
Bertrand firm cannot maintain price
• Consider a market entry game
can a market be pre-empted by a first-mover?
• Take a simple example
two companies Microhard (incumbent) and Newvel (entrant)
Newvel makes its decision first
enter or stay out of Microhard’s market
Microhard then chooses
accommodate or fight
pay-off matrix is as follows:
Credibility and predation
• Options listed are strategies not actions
• Microhard’s option to Fight is not an action
• It is a strategy
Microhard will fight if Newvel enters but otherwise remains placid
• Similarly, Accommodate is a strategy
defines actions to take depending on Newvel’s strategic choice
• Are the actions called for by a particular strategy credible
Is the promise to Fight if Newvel enters believable
If not, then the associated equilibrium is suspect
• The matrix-form ignores timing.
represent the game in its extensive form to highlight sequence of moves
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The chain-store paradox
• What if Microhard competes in more than one market?
threatening in one market one may affect the others
• But: Selten’s Chain-Store Paradox arises
20 markets established sequentially
will Microhard “fight” in the first few as a means to prevent entry in later ones?
No: this is the paradox
Suppose Microhard “fights” in the first 19 markets, will it “fight” in the 20 th?
With just one market left, we are in the same situation as before
“Enter, Accommodate” becomes the only equilibrium
Fighting in the 20th market won’t help in subsequent markets . . There are no subsequent markets
So, “fight” strategy will not be adapted in the 20th market
• Now consider the 19th market
Equilibrium for this market would be “Enter, Accommodate”
The only reason to adopt “Fight” in the 19th market is to convince a potential entrant in the 20th market
that Microhard is a “fighter”
But Microhard will not “Fight” in the 20th market
So “Enter, Accommodate” becomes the unique equilibrium for this market, too
• What about the 18th market?
“Fight” only to influence entrants in the 19th and 20th markets
• But the threat to “Fight” in these markets is not credible.
“Enter, Accommodate” is again the equilibrium
• By repetition, we see that Microhard will not “Fight” in any market